The present invention relates to a method of obtaining a signal which represents the phase difference between a local carrier or oscillator signal and the carrier of an amplitude and/or phase shift keyed received signal having a plurality of possible signal states. More particularly, the present invention relates to a method of the above type wherein signal representing the received signal is initially divided into a pair of cartesian coordinate signal components (x, y) which are a function of the phase difference and are in quadrature relationship to one another, with the two signal components together representing one of the possible signal states, and wherein the pair of cartesian coordinate signal components (x, y) is thereafter converted into a corresponding pair of polar coordinate signal components (R, .alpha.), with one of the polar signal components representing the amplitude (R) of a signal state vector formed by the pair of cartesian coordinate signal components (x, y) while the other polar signal component represents the phase angle (.alpha.) for this signal state vector.
Such a method for obtaining a control signal for a voltage controlled oscillator employed for carrier recovery in a demodulator circuit for amplitude and/or phase shift keyed (QASK) signals, is disclosed generally in an article by M. Hoffmann, entitled "Carrier Recovery for m-QAM Signals", in ECRR, pages 247-253, published by vde-Verlag, Munich, November 1986, and more specifically in Applicant's copending U.S. patent application Ser. No. 07/062,366 filed June 12, 1987, the subject matter of which is incorporated herein by reference.